"Hard clipping" was probably a poor word choice, but it's hard to come up with a way to say it. Maybe some examples.
It's possible to come up with a test tone which is demanding enough of power to keep the caps from building up a full charge, and the current flow has saturated the transformer's core. At this point the peaks of the output waveform start clipping. This is all the power that can be moving through the amp to the speaker at any instance in time. Turning the volume up higher will result in a higher power RMS reading, but the instantaneous power reading will be no higher. It is just the amp is spending more time at its peak output. Instead of just the absolute peaks being clipped some of the lower portions of the signal have gone to DC too.
The other example is a passage which is nearly silent, the caps have a good charge built up, the transformer is far from saturation. Then a shot rings out. This spike in the output can exceed the the level of that continuous bombardment mentioned above.
Most content is more like the second example. A few small peaks with most of the signal not being very demanding. So you may not have a huge power reserve, but you can exceed the levels of what one gets with a test signal. As you turn up the volume further where the amplifier is reaching its limits for this content, the loss of a few little peaks is hardly noticeable. As that happens the lower portions are still getting louder and taking more power to reproduce. It's not until more of the signal is clipped that you think things are starting to sound harsh, and (hopefully) back off a little.
I still don't know if I'm doing a good job describing this. Maybe if you think of sound as being made of lots of little instances, but the power readings are taken with that averaged over time. The more time spent at higher output levels the higher the Watts RMS reading. So if even the tiny peaks are clipping because the amp can't exceed the current flow at that instant in time, it doesn't mean that more power can't be applied to bring more parts of the signal up in level.
